After burning through live versions of 10 of the 12 tracks on their recently-released debut CD (“Edgar Meyer & Chris Thile”), plus a few Bach numbers for good measure, double-bassist Meyer and mandolinist Thile turned to their audience at Benaroya Hall for, well, help.

Could anyone in the house think of a theme or topic that might generate a new composition?

Meyer, the first bassist to win the Avery Fisher Prize for outstanding achievement in classical music (alongside a MacArthur Foundation “Genius” Award and three Grammy Awards), and Thile, also a Grammy winner with a following in the bluegrass, country and classical worlds, playfully entertained ideas.

Inspiration taken, they set off on a performance that, like everything else they played Monday night, showcased the rigorous yet accessible, and engrossing, experimentation that defines their intermittent partnership.

There is an inevitability to Meyer and Thile’s collaboration. Meyer, 47, is equally at home playing double bass for classical music as well as jazz and folk. He has sought ways to fuse improvisation with formal structure.

Thile, 27, a founding member of the popular bluegrass groups Nickel Creek and Punch Brothers, has been attempting the same thing from another direction. The two men have performed, together and separately, with some of the same artists (Béla Fleck, Mark O’Connor), and Thile wrote a piece for double bass and piano that Meyer and Emanuel Ax premiered last year.

With the new album and tour, Meyer and Thile are realizing the potential of the music they began exploring years ago. Their almost unclassifiable sound at Benaroya refused to lock onto fleeting influences, and they focused primarily on the dynamics of performing together.

As with some types of jazz and even rock, Thile and Meyer sometimes blended their sounds, then at other times drove one another way from synthesis.

The show’s most exciting moments revealed sudden eruptions of possibility and poetry. The concert began with grey, almost-sunrise tones from the bass, while Thile’s mandolin danced steadily around the sound. Abruptly, Meyer opened up, and Thile soon followed. Patterns emerged and then blurred like a stone tossed into a watery reflection.

The music similarly morphed all night — scattered, grinding, bluesy, minimalist — and the two stars invoked structures and quickly dispensed with them. Their forays into Bach temporarily cooled the fever of improvisational adventures, but the boldness of this duo’s performance will not be easily forgotten.